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        riddles >> medium >> coin orgy
        
(Message started by: Moti on Nov 24^th, 2002, 1:49pm)

Title: coin orgy
Post by Moti on Nov 24^th, 2002, 1:49pm

placing 1 or 2 or 3 or even 4 coins so that every coin touches all the rest is not too difficult.
try doing that with 5 coins.

Title: Re: coin orgy
Post by Chronos on Nov 24^th, 2002, 6:52pm

Head on over to the "hard" forum. There's a thread pinned to the top on "cigarettes max clique", which eventually generalizes to cylinders of any length. Since a coin is just a really short cylinder, the answer there, that it's impossible to get more than 4, applies.

Title: Re: coin orgy
Post by Moti on Nov 25^th, 2002, 12:58am

oh really???

and what if i told you there is a way of doing that?

would it make you start thinking?

Title: Re: coin orgy
Post by towr on Nov 25^th, 2002, 1:21am

you could always mutilate the coins.. Have a train run over them, then role them up like sigarettes :p
or melting them into each other..

Are the coins the same size? Else you could place two coins on top of each other, and three around them (but those would have to be larger)

Title: Re: coin orgy
Post by Moti on Nov 25^th, 2002, 5:34am

:-)

no, the coins are not melted and yes they are the same size

(no trick to this one guys)

Title: Re: coin orgy
Post by towr on Nov 25^th, 2002, 6:37am

hmm.. I think I can manage it.. But it's hard to keep the coins in place..

also, the flatter the coin (relative to the diameter) the easier..

Title: Re: coin orgy
Post by Garzahd on Nov 25^th, 2002, 1:13pm

Say the coins are circles of radius 1 and low thickness.
Put coin 1 on the origin.
Put coin 2 centered at (1,0) and coin 3 at (-1,0), both of these on top of coin 1.
Coin 4 and 5 form a little tepee on top of the other three, symmetric across the X-axis.

This apparatus is very hard to replicate with actual coins, though if you add extra coins to support 2 and 3 to prevent them from falling over, it's not too bad.

Title: Re: coin orgy
Post by Moti on Nov 25^th, 2002, 2:11pm

If i was cartman i'd probably say...

"I love you guys..."

the solution is correct! :D ;D :D

Title: Re: coin orgy
Post by SWF on Nov 25^th, 2002, 9:46pm

If it is not considered cheating, there are a couple of other ways which require more than two coins to touch at a single point, and also require the coins be perfect cylinders instead of real coins.

Place coins 1 and 2 flat on the table touching each other. On top of them balance coin 3 on edge exactly on the point where 1 and 2 touch. Put coins 4 and 5 touching each other flat on top of coin 1. Slide 4 and 5 until they both touch coin 3. After moving 4 and 5 in contact with 3 they will also overlap with coin 2 if the coins are thin enough.

It looks like it works with disks the size of quarters, but not nickels. Nickels also appear to be too thick for the tepee method. Maybe somebody can figure out how thin the coins need to be for each method to work.

With four coins touching at a point, thickness doesn't matter. Place four coins in adjacent stacks of two. Hold the fifth coin half a coin thickness off the table so it is tangent to all four.